I would say trying to cook 3x faster isnt a surface temp 3x higher, but the rate of heat transfer is 3x faster. Because then your laat step is backwards.
Q = h a dT
If you just calculated H goes up 1.69x, then dT doesnt need to go up MORE, it needs to go up LESS. A higher HTC increases the rate of heat transfer. Which… now you need to recalc your free conv HTC because temp changed. But if it didnt…
3Q = 1.69h a 1.78DT
Old DT was 260, now its 463, which is an ovev temp of 503F
Edit: this is a transient problem we’re trying to reduce to a steady state calculation with pretty poorly defined requirements. Sounds like a typical day at work for me lol
True, temperature was just the main part of the meme and a higher temp is funnier anyway so I went with it lol
Also for a transient solution, idk the avg thermal conductivity of a whole chicken, which we’d need for a one-term approximation if we assumed the chicken was a sphere of homogeneous material.
If we really wanted to be accurate, an FDM model probably wouldn’t be too hard to setup, and would let us more accurately account for changes in both the transient convection and the change in conductivity of the meat with temp. But I’m not motivated enough just to do all that for a nonsense problem lol
Then again I doubt we’d be able to create the exact same transient response just scaled by 3x without having to modify the setup since the insulation by the skin goes up as the fat melts (or is vaporized) and replaced by air which would happen sooner as we increase the temperature.
When I read ‘isnt a surface temp’ I instantly think of heat pipes you can run through the chicken to increase heat transfer from outside to inside. Not sure if that’s how anyone does it, but I wouldn’t be surprised if something like that is used somewhere
I would say trying to cook 3x faster isnt a surface temp 3x higher, but the rate of heat transfer is 3x faster. Because then your laat step is backwards.
Q = h a dT
If you just calculated H goes up 1.69x, then dT doesnt need to go up MORE, it needs to go up LESS. A higher HTC increases the rate of heat transfer. Which… now you need to recalc your free conv HTC because temp changed. But if it didnt…
3Q = 1.69h a 1.78DT
Old DT was 260, now its 463, which is an ovev temp of 503F
Edit: this is a transient problem we’re trying to reduce to a steady state calculation with pretty poorly defined requirements. Sounds like a typical day at work for me lol
True, temperature was just the main part of the meme and a higher temp is funnier anyway so I went with it lol
Also for a transient solution, idk the avg thermal conductivity of a whole chicken, which we’d need for a one-term approximation if we assumed the chicken was a sphere of homogeneous material.
If we really wanted to be accurate, an FDM model probably wouldn’t be too hard to setup, and would let us more accurately account for changes in both the transient convection and the change in conductivity of the meat with temp. But I’m not motivated enough just to do all that for a nonsense problem lol
Then again I doubt we’d be able to create the exact same transient response just scaled by 3x without having to modify the setup since the insulation by the skin goes up as the fat melts (or is vaporized) and replaced by air which would happen sooner as we increase the temperature.
When I read ‘isnt a surface temp’ I instantly think of heat pipes you can run through the chicken to increase heat transfer from outside to inside. Not sure if that’s how anyone does it, but I wouldn’t be surprised if something like that is used somewhere